municipal school; city-run school
Refers to a school founded and managed by a city government, as opposed to a prefectural or national school. Often contrasted with 私立学校 (private school).
This municipal school has new facilities.
To become a teacher at a city-run school, you need to pass the city's employment exam.
私立学校 is a private school, while 市立学校 is a public school run by a city. The readings are identical, so context or kanji is needed to distinguish them.
公立学校 is a broader term for any public school (including prefectural and national), whereas 市立学校 specifically refers to those established by a city.
Compound of 市立 (しりつ, 'municipal') + 学校 (がっこう, 'school'). The reading しりつ is shared with 私立 (private), so context or the kanji 市 is essential to distinguish them.